Big-O notation - Factbites

Big-O notation - Factbites
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Topic: Big-O notation

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	Big O notation - Wikipedia, the free encyclopedia
		Big O notation is a mathematical notation used to describe the asymptotic behavior of functions.
		Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informal substitute for Θ (Theta, see below).
		Big O notation is useful when analyzing algorithms for efficiency.
	en.wikipedia.org /wiki/Big_O_notation (1280 words)

	PlanetMath: Landau notation
		O notation, omega notation, theta notation, big-O notation
		This is version 12 of Landau notation, born on 2001-10-06, modified 2005-10-07.
		In analysis, such notation is useful in describing error estimates.
	planetmath.org /encyclopedia/BigONotation.html (185 words)

	Big O Notation
		Big O notation is a method of rating the speed or efficiency of various algorithms.
		As a final note on Big - O notation, one must address the idea of algorithmatic efficiency.
		Computer scientists consider an algorithm to be efficient if it executes in polynomial time, that is, if its Big-O function is a polynomial.
	home.att.net /~quam1/physics/Physics/Physics/Prelim/big_o_notation.htm (441 words)

	Big O - Wikipedia, the free encyclopedia
		Big O Tires, a tire company in the United States.
		The Big O, a Roy Orbison album, or Roy Orbison himself.
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/Big_O (115 words)

	Algorithm Analysis and Big-O Notation
		Big O notation, also called an efficiency indicator, is used to describe the growth rate of a function.
		The big O notation represents the running time needed to solve the computational steps.
		One way to derive these formulas is the big O notation.
	www.programcpp.com /AppendixE/E_1.html (103 words)

	Big-O Notation and Algorithm Analysis
		Although big-O notation is a way of describing the order of a function, it is also often meant to represent the time complexity of an algorithm.
		Now that we have seen the basics of big-O notation, it is time to relate this to the analysis of algorithms.
		For example, when we are analyzing an algorithm that multiplies two numbers, the functions we might be interested in are the relationships between the number of digits in each number and the length of time or amount of memory required by the algorithm.
	www.eecs.harvard.edu /~ellard/Q-97/HTML/root/node8.html (876 words)

	Math Forum - Ask Dr. Math
		Date: 04/12/2001 at 10:17:29 From: Paul Statham Subject: Big O Notation and polynomials I have a sample question I have been practicing.
		Date: 04/12/2001 at 17:31:19 From: Doctor Rob Subject: Re: Big O Notation and polynomials Thanks for writing to Ask Dr. Math, Paul.
		This bit is confusing me because if that is the case, then how can g(x) be O(f(x)) ?
	mathforum.org /library/drmath/view/54501.html (658 words)

	big-O notation
		The notation is read, "f of n is big oh of g of n".
		Paul E. Black, "big-O notation", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
		Donald E. Knuth, Big Omicron and Big Omega and Big Theta, SIGACT News, 8(2):18-24, April-June 1976.
	www.nist.gov /dads/HTML/bigOnotation.html (462 words)

	AP CS Big-O
		Big-O notation essentially allows you to compare the time of execution for various computer processes as they tie up the use of the microprocessor.
		O (f(n)) is the Big-O for a specific function f(n)
		See if the new set if 5 times as big (1000 * 5 = 5000) and the algorithm is an n
	dimacs.rutgers.edu /~rkrane/clecs/apa/bigO.html (841 words)

	Data Structures Notes: Big O
		The motivation behind Big-O notation is that we need some way to measure the efficiency of programs but there are so many differences between computers that we can't use real time to measure program efficiency.
		Big-O notation makes use of dominant terms like this to create several classes of functions that serve as general measures of algorithm efficiency.
		And no matter how big it is, it will not turn the quadratic into an exponentional function.
	starbase.trincoll.edu /~ram/cpsc215/notes/bigO.html (570 words)

	SparkNotes: Searches and Efficiency: Efficiency and Big-O notation
		When discussing the efficiency of an algorithm, there are three cases that need to be considered: the best case, the worst case, and the average case.
		To describe the order of magnitude of a function, we use Big-O notation.
		If we had an algorithm that did 2n + 5 operations, the big-O notation would be O(n).
	www.sparknotes.com /cs/searching/efficiency/section3.rhtml (466 words)

	Math Forum - Ask Dr. Math
		Date: 12/12/2000 at 11:26:13 From: Doctor Ian Subject: Re: Matrix multiplication done in big-O notation Hi Peter, Big-O notation is just a way of being able to compare expected run times without getting bogged down in detail.
		I'm very familiar with matrix multiplication, but I've never worked with big-O notation, so any help would be greatly appreciated.
		This notation, then, is used to compare algorithms in terms of speed: An O(n) algorithm is faster than an O(n^2) algorithm, but slower than an O(log n) algorithm.
	mathforum.org /library/drmath/view/51904.html (403 words)

	big O notation - Neowin.net
		Big O notation represents the max number of iterations(not really the word I want to use) of an algorithm.
		I learned the big O notation in class, but I still don't understand it.
		I understand the point of big o notation and what you have said.
	www.neowin.net /forum/index.php?showtopic=178833 (693 words)

	WebDeveloper.com - Big O Notation
		In learning about Big O notation, I have to identify which formula each method would use.
		The concept of Big O notation is simple.
		The concept of Big O is quite confusing to me, but i've given a go at it, and was wondering if anyone could provide some correction/suggestions/advice.
	www.webdeveloper.com /forum/showthread.php?p=335286 (1532 words)

	Big O Notaion
		Since O(log x) is the smaller of the two, O(log x) is the least upper bound and "official" O. See page 82 for a discussion of this.
		If terms are added, the O is the O of the largest O of the terms.
		What we would like is to develop algorithms that have the smallest O values.
	www.wpunj.edu /wpcpages/irt/courses/CS260rv/cs_big_O.htm (383 words)

	Big-O notation (was: Re: Python and Schools)
		Previous message: Big-O notation (was: Re: Python and Schools)
		Next message: Big-O notation (was: Re: Python and Schools)
	mail.python.org /pipermail/python-list/2003-April/158521.html (172 words)

	bigO.txt
		The most common place that big-Oh notation is used in computer science is in giving estimates for the running time for algorithms.
		First remember that big-O notation gives a measure of how fast a function is increasing as it gets large.
		From P. Barry, Class notes for CSci 2011 ADDITIONAL COMMENTS ON BIG-O NOTATION Many student find big-O notation confusing --- and the definition is complicated --- so here are some additional comments on it.
	www-users.itlabs.umn.edu /classes/Spring-2002/csci2011/bigO.txt (426 words)

	Big-O and notation
		notation there is no need to specify the base of logarithms--all versions are equally valid.
		Note that neither notation says anything about f(n) being a computing time estimate, even though that will be a common use.
		Big-O just provides an upper bound to say that f(n) is less than something, while
	www.cl.cam.ac.uk /Teaching/1998/InroAlgs/notes98/node6.html (430 words)

	question about big O notation in data structures - PointAsk Question
		Big O notation, for polynomials, is just the highest-order term from the polynomial, without a coefficient.
		question about big O notation in data structures
		question about big O notation in data structures- PointAsk Question
	www.pointask.com /pointask/f_q.php3?qid=55243 (155 words)

	Preserved Topic: Big O Notation — OZONE Asylum, home of the Mad Scientists
		Big O notation is no little topic many people spend their entire live analysing algorithms efficiencies.
		O(c) makes no sence in big O notation, since constants are ignored.
		They taught Big O in CS1; Omega, Theta, little o, and 1 other in CS2; and now they are going deeper into Big O in CS3.
	www.ozoneasylum.com /17366 (1452 words)

	IB CS
		This notation, known as big-O notation, is a typical way of describing algorithmic efficiency; note that big-O notation typically does not call for inclusion of constants.
		We will describe big-O notation, and show how big-O bounds can be computed for some common algorithms.
		As long as it’s a linear function which is proportional to N, the correct notation is O(N) and the code is said to have linear running time.
	www.eca.com.ve /ibcs2/bigO.htm (2752 words)

	Perl.com: Optimizing Your Perl
		There are other notations to represent the magnitude of minimum and actual runtimes.
		Returning to the big picture, we need to take our message-id cache size into account when determining the method to use.
		It was easy to implement and worked very well, until the graph got very big.
	www.perl.com /lpt/a/2002/02/12/bigo.html (1447 words)

	[texhax] "big O" and "little O" notation in amsmath
		This big-O notation was introduced by P. Brachmann in 1894.
		The little-oh notation was first used by E. Landau in 1909.
		This intuitively means that the error in using g(x) to approximate f(x) is negligible in comparison to h(x).
	www.tug.org /pipermail/texhax/2004-January/001491.html (501 words)

	Big-O_notation
		Thus, in Big-O notation, this algorithm is "Big-O of n" or O(n).
		This example simply helps to explain why Big-O notation can give a very helpful rough idea of the time-complexity of an algorithm, even though you may not know any specific run-times.
		only the largest term in the expression counts for Big-O notation!
	cs.gmu.edu /~jotten/cs211/slides/Big-O_notation.html (958 words)

	RE: Big-O notation - dBforums
		O() ::=3D The big-O notation gives an indication of the growth=20
		dBforums > Usenet Groups > comp.lang.* > comp.lang.python > RE: Big-O notation
	www.dbforums.com /t757186.html (155 words)

	Dictionary of Algorithms and Data Structures
		The two-level index has a total download 1/20 as big as this page.
		We thank those who contributed definitions as well as many others who offered suggestions and corrections.
		A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
	www.nist.gov /dads (594 words)

	Complexity and Big-O Notation
		Recall that when we use big-O notation, we drop constants and low-order terms.
		This is because when the problem size gets sufficiently large, those terms don't matter.
		O(N): assuming each item equally likely to be current
	www.cs.wisc.edu /~hasti/cs367-common/notes/COMPLEXITY.html (2435 words)

	Turing machine
		See also other models: cell probe model, random access machine, pointer machine, multiprocessor model, related terms: big-O notation, busy beaver, variants: alternating Turing machine, nondeterministic Turing machine, oracle Turing machine, probabilistic Turing machine, universal Turing machine.
		Unless otherwise specified, a Turing machine is deterministic.
		Note: From Algorithms and Theory of Computation Handbook, page 24-19, Copyright © 1999 by CRC Press LLC.
	www.nist.gov /dads/HTML/turingMachine.html (189 words)

	Big-O Notation, Java Q & A Archive, Perry Smith
		The notation used to describe the amount of work that a function does as its input size inreases is expressed as big omega, big theta, or big O (or big oh.)
		Big O (f) - a function given this designation will cause the amount of work done by that function to grow no faster than the function f as the input size rises.
		Big Omega (f)- functions given this designation will grow at least as fast as function f.
	www.perryland.com /question220.html (189 words)

	Big-O_notation
		Thus, in Big-O notation, this algorithm is "Big-O of n" or O(n).
		This example simply helps to explain why Big-O notation can give a very helpful rough idea of the time-complexity of an algorithm, even though you may not know any specific run-times.
		only the largest term in the expression counts for Big-O notation!
	cs.gmu.edu /~maney/cs211/SLIDES/Big-0_notation.html (189 words)

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